Kinematics, workspace and singularity analysis of a multi-mode parallel robot

A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lock-able P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.

[1]  Pietro Fanghella,et al.  Parallel robots that change their group of motion , 2006, ARK.

[2]  Xianwen Kong,et al.  Reconfiguration analysis of a 3-DOF parallel mechanism using Euler parameter quaternions and algebraic geometry method , 2014 .

[3]  Damien Chablat,et al.  Design Strategies for the Geometric Synthesis of Orthoglide-type Mechanisms , 2007, ArXiv.

[4]  C. Gosselin,et al.  Type Synthesis of Parallel Mechanisms With Multiple Operation Modes , 2007 .

[5]  George E. Collins,et al.  Quantifier elimination for real closed fields by cylindrical algebraic decomposition , 1975 .

[6]  Xianwen Kong,et al.  Type Synthesis of 3-DOF Multi-Mode Translational/Spherical Parallel Mechanisms with Lockable Joints , 2016 .

[7]  Jian S. Dai,et al.  Advances in Reconfigurable Mechanisms and Robots II , 2012 .

[8]  Xianwen Kong,et al.  Type Synthesis of Two-Degrees-of-Freedom 3-4R Parallel Mechanisms With Both Spherical Translation Mode and Sphere-on-Sphere Rolling Mode , 2015 .

[9]  Manfred Husty,et al.  Reconfiguration analysis of a 4-RUU parallel manipulator , 2016 .

[10]  Fabrice Rouillier,et al.  Solving parametric polynomial systems , 2004, J. Symb. Comput..

[11]  Hieu Minh Trinh,et al.  Two-mode overconstrained three-DOFs rotational-translational linear-motor-based parallel-kinematics mechanism for machine tool applications , 2007, Robotica.

[12]  Michel Coste,et al.  Extra Modes of Operation and Self-Motions in Manipulators Designed for Schoenflies Motion , 2015 .

[13]  Jian S. Dai,et al.  Geometric Constraint and Mobility Variation of Two 3SvPSv Metamorphic Parallel Mechanisms , 2013 .

[14]  Damien Chablat,et al.  An Interval Analysis Based Study for the Design and the Comparison of 3-DOF Parallel Kinematic Machines , 2007, ArXiv.

[15]  Xianwen Kong,et al.  Type Synthesis of Variable Degrees-of-Freedom Parallel Manipulators With Both Planar and 3T1R Operation Modes , 2012 .

[16]  Jian S. Dai,et al.  Mobility Change in Two Types of Metamorphic Parallel Mechanisms , 2009 .

[17]  Xianwen Kong.  Reconfiguration Analysis of a Variable Degrees-of-Freedom Parallel Manipulator With Both 3-DOF Planar and 4-DOF 3T1R Operation Modes , 2016 .

[18]  F. Pierrot.  Modelling and design issues of a 3-axis parallel machine-tool , 2002 .

[19]  Kornel Ehmann,et al.  Design of parallel hybrid-loop manipulators with kinematotropic property and deployability , 2014 .

[20]  Qinchuan Li,et al.  Parallel Mechanisms With Bifurcation of Schoenflies Motion , 2009, IEEE Transactions on Robotics.

[21]  X. Kong.  Type Synthesis of 3-DOF Parallel Manipulators With Both a Planar Operation Mode and a Spatial Translational Operation Mode , 2013 .

[22]  Damien Chablat,et al.  Kinematics and workspace analysis of a three-axis parallel manipulator: the Orthoglide , 2005, Robotica.

[23]  Xianwen Kong,et al.  Reconfiguration analysis of a 4-DOF 3-RER parallel manipulator with equilateral triangular base and moving platform * , 2016 .

[24]  Xianwen Kong,et al.  Type Synthesis of 3-DOF PPR-Equivalent Parallel Manipulators Based on Screw Theory and the Concept of Virtual Chain , 2005 .

[25]  M. Callegari,et al.  A new class of reconfigurable parallel kinematic machines , 2014 .

[26]  Wei Ye,et al.  A new family of reconfigurable parallel mechanisms with diamond kinematotropic chain , 2014 .

[27]  Maurizio Ruggiu,et al.  Mobility and kinematic analysis of a parallel mechanism with both PPR and planar operation modes , 2012 .

[28]  Jian S. Dai,et al.  Geometry constraint and branch motion evolution of 3-pup parallel mechanisms with bifurcated motion , 2013 .

[29]  Grigore Gogu,et al.  Maximally Regular T2R1-Type Parallel Manipulators With Bifurcated Spatial Motion , 2011 .

[30]  Fabrice Rouillier,et al.  Cusp Points in the Parameter Space of Degenerate 3-RPR Planar Parallel Manipulators , 2012, ArXiv.

[31]  Manfred Husty,et al.  A complete kinematic analysis of the SNU 3-UPU parallel robot , 2009 .

[32]  Damien Chablat,et al.  Definition sets for the direct kinematics of parallel manipulators , 1997, 1997 8th International Conference on Advanced Robotics. Proceedings. ICAR'97.

[33]  Damien Chablat,et al.  Working modes and aspects in fully parallel manipulators , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).